Browsing by Subject "Ring gyroscope"

Now showing 1 - 6 of 6

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Analytical and experimental study of stress effects in a MEMS ring gyroscope
(Elsevier, 2023-09-09) Hosseini-Pishrobat, Mehran; Erkan, Derin; Tatar, Erdinc
External stress affects the stiffness distribution of a MEMS gyroscope and, along with temperature, is affiliated with long-term drift. Although the detrimental effects of stress on MEMS gyroscopes are well-documented, modeling of such effects is still lacking in the literature. For the first time, we present an analytical model that mathematically describes the stress effects in a ring gyroscope. Our model revolves around the key observation that stress-induced anchor displacements result in variations of electrostatic gaps and nonhomogeneous boundary conditions at the interface between the gyroscope’s suspension system and the anchored internal structure. Our gyroscope is equipped with 16 capacitive stress sensors distributed with 45° symmetry on the inside and outside of the main ring. We use these stress sensors’ measurements to interpolate the strain field across the substrate and deduce the anchor displacements. To capture the stress effects, we show that two fundamental assumptions in the existing literature should be amended: (1) Linearity: the linear engineering strain should be upgraded to the nonlinear Green–Lagrange strain to reveal the stress-induced stiffness through geometric nonlinearity; (2) Inextensibility: for a ring, this stress stiffness is determined by the extensional stress arising from centerline extensibility. We analyze variations of frequencies and mode shapes’ orientation along with the resultant quadrature and in-phase errors. Moreover, we present a fairly general formulation incorporating fabrication-induced imperfections and elastic anisotropy. We validate our model experimentally using extensive bending tests performed on our 59 kHz, 3.2 mm diameter gyroscope.
Open Access
A MEMS vibrating ring gyroscope with on-chip capacitive stress sensors for drift compensation
(2022-07) Uzunoğlu, Baha Erim
MEMS gyroscopes are commonly used for rotation measurement in navigation. Even though the noise performance of these sensors has improved in the last few decades, the long-term drift problem is still prominent for these sensors. Longterm drift error is caused by external factors such as temperature and induced stress on the MEMS chip. With this work, we present an on-chip solution for the compensation of long-term drift. Due to its compact and singular anchor morphology, a vibrating ring gyroscope design was employed. Eight bridge-type capacitive stress sensors were placed periodically at the inner section of the ring surrounding the inner anchor, which adds localized stress measurement capability to the design. Another eight stress sensors were placed at the outer section of the ring surrounding the electrodes of the device. Tensile stress was applied on a testbed, and the output of the stress sensors and the gyroscope were recorded. Then, the gyroscope was subjected to a zero rate output(ZRO) test in mismatch and matched frequency configurations. The compensated output of the device was able to reach 0.008 /h in mismatched mode and 0.003 /h in matched mode without any signs of drift. The stress and the gyroscope output were partitioned into 12 hour blocks to increase the performance of the least squares fitting algorithm. We have observed a decrease in the compensation performance due to possible nonlinear and hysteresis effects generated during the long-term operation. Finally, we were able to show that the change in temperature wasn't sufficient enough to explain the frequency change of the drive and sense modes.
Open Access
Modeling stress effects on frequencies of a MEMS ring gyroscope
(IEEE, 2023-03-01) Hosseini-Pishrobat, Mehran; Uzunoğlu, Baha Erim; Tatar, Erdinç
We present, for the first time, an analytical model for the external stress effects on the frequencies of a vibrating ring gyroscope (VRG). The stress-induced anchor displacements cause gap changes in the electrodes and nonhomogeneous boundary conditions in the VRG’s suspension structure. Stress stiffness arising from the geometric nonlinearity in the suspension is the principal mechanism affecting VRG’s frequencies as it dominates variations of the electrostatic softening. We validate our model using external stress tests performed on a 57kHz VRG equipped with 16 symmetrically distributed, on-chip capacitive stress sensors, which provide anchor displacement measurements.
Open Access
Modeling temperature effects in a MEMS ring gyroscope: toward physics-aware drift compensation
(Institute of Electrical and Electronics Engineers, 2025-01-15) Hosseini-Pishrobat, Mehran; Tatar, Erdinç
Temperature plays an indispensable role in the long-term performance of MEMS gyroscopes, and despite extensive studies in the literature, analytical treatment of temperature effects is still an open problem. This paper, to the best of our knowledge, is the first attempt to address this gap for ring gyroscopes. We start with a superposition principle that disentangles thermal displacement fields from the gyroscope's nominal vibration. We set forth a geometrically nonlinear variational formulation to obtain the temperature-induced stiffness matrix. We conduct temperature tests on our 3.2 mm-diameter, 58 kHz ring gyroscopes equipped with 16 capacitive stress sensors. The experimental data validate our analytical modeling in the following key aspects: 1) The model accounts for not only changes in material properties but also a less explored factor, thermal stresses. Thanks to a strain interpolation module that leverages the measured stresses, the model predicts frequency variations consistently and captures hysteresis loops arising from residual stresses. Notably, we accurately estimate the deviation of the temperature coefficient of frequency (TCF) from the expected value -30 ppm/C-degrees (based on the widely known -60 ppm/C-degrees dependency of Young's modulus of silicon). 2) The model is able to capture stiffness couplings in the orders of less than 0.1 N/m (in a 7 kN/m device) and closely predicts the quadrature error and its leakage into the in-phase channel. Additionally, the model incorporates temperature variations of mechanical scale factor, drive mode's amplitude, damping coupling, and sense mode's phase in terms of their contribution to the in-phase error. Based on these merits, our model serves as a building block toward drift compensation algorithms encompassing the underlying physics of the temperature effects.
Open Access
On temperature effects in a mems ring gyroscope
(2024-04-23) Hosseini-Pishrobat, Mehran; Tatar, Erdinç
We report on experimental and analytical investigation of temperature effects in a 3.2mm-diameter, 57kHz ring gyroscope equipped with 16 capacitive stress sensors. According to the well-known ~-60ppm/°C temperature dependency of Young’s modulus of silicon, the temperature coefficient of frequency (TCF) is expected to be ~-30ppm/°C. Our experimentally observed TCFs, however, tend to be ~-14ppm/°C, pointing to thermal stresses as the countering factor. To find the root cause of the measured TCFs, we develop an analytical framework that enables us to calculate the temperature-induced stiffness variations, considering both thermal and mechanical strains. The model successfully predicts changes and hysteretic behavior of frequency over temperature using the measured stress and temperature data.
Open Access
A ring gyroscope with on-chip capacitive stress compensation
(Institute of Electrical and Electronics Engineers, 2022-08-18) Uzunoğlu, Baha Erim; Erkan, Derin; Tatar, Erdinç
We present long-term stress compensation results for a 3.2mm diameter ring gyroscope integrated with 16 capacitive stress sensors for the first time in this work. A bridge-type capacitive sensor is preferred due to its compact size and temperature insensitivity for on-chip stress measurements. The ring design enables a high level of integration and stress sensor-gyroscope output correlation. We first demonstrate the stress sensor operation on a stress test-bed. The drift test for sixteen days at mismatched mode and the drift test for eight days at matched mode in room temperature reveal that the stress compensation can eliminate the gyroscope drift. The stability of the stress compensated gyroscope output can reach 0.008°/h in mismatched mode and 0.003°/h in matched mode at an averaging time of two days with no signs of long-term drift. High gyroscope stability is achieved with a partial least-squares fitting algorithm; however, we believe that stress and gyroscope output relation might be linear time-variant with possible nonlinear and hysteresis effects. Analysis of the drive and sense mode frequencies shows that only temperature cannot explain the frequency variations, and the inclusion of stress can comprehensively describe the frequency changes.